Thought experiments - simple to carry out (no equipment, so to speak, needed), but the results can be profound. Thought experiments lead to Einstein formulating special relativity, in other cases they are useful in demonstrating or refuting otherwise abstruse laws of physics. For example Maxwell's Demon and Feynmann's Brownian Ratchet both require or lead to analyses of the second law of thermodynamics; Bell's spaceship considers relativity and so on. Then there are many famous examples in quantum mechanics, notably Schroedinger's cat.
Of course one of the better advantages of the thought experiment arises from its position as a theoretical or analytical tool. As the experiment takes place in one's mind, we can happily ignore the limitations of the practical, the current state of engineering and anything else we like, provided we don't break the laws of physics.
Although thought experiments are most common in physics, the technique can be used in other fields to expose what is essentially ridiculous. Here we consider what may at first appear to be an unlikely topic: British Law, or at least that part of it that prevents us from returning anyone to their country of origin if they are thought likely to face torture or be executed. This is the case no matter what laws they may have broken before fleeing, nor how heinous their activities on British soil are, no matter what hatred or violence they incite or have incited in the past, no matter what laws they may break whilst over here.
Consider this hypothetical case: a citizen of some unnamed country that has the death penalty is a terrorist. Whilst at large he perpetrates a number of outrages both against his own country and others; large numbers of entirely innocent people die. During the course of one attack the authorities in his country manage to gather absolutely convincing evidence of his guilt, but don't manage to capture him. What is the best course of action for this terrorist?
Well if he stays he will be captured, tried, convicted and put to death, so best not to hang around. Question is where to go..? Well clearly he'd prefer some absolutist regime that more or less supports his aims and will therefore harbour him. However such places do tend to be unstable, so he thinks he should look around for somewhere better. At this point a lawyer points out the British Law mentioned above, so he comes over here.
At first he lives a blameless life, he breaks no UK laws and lives undiscovered. Then his identity is exposed and he is arrested, however he has committed no crime within UK jurisdiction so the only option is to extradite him. But, of course, we can't because his home country will clearly execute him, so what happens..? We have to shelter him!
Another example: two identical crimes are committed in a foreign jurisdiction, by identical criminals in identical circumstances (OK, unlikely I know, but you see the advantage of the thought experiment...). They are both tried in identical ways and sentenced to identical punishments, death in this case. Only now do the cases diverge, one criminal escapes the other does not. The one that escapes gets to the UK, he is extradited but the terms of the extradition are that he must not be executed once he is returned; the other criminal is executed. Clearly we have created an unjust situation. Either one criminal has been unfairly executed, or the other has been unfairly reprieved or possibly a society has been unfairly deprived of its right to act according to its own laws.
Another example, this time with a real character. Imagine after his trial but before his execution Saddam Hussein escapes (this is a thought experiment, so we don't need to consider how, in theory it's possible). Where does he go?
Why he comes here of course and our laws prevent us from returning him to Iraq. So after all that time, effort and money spent removing him from power, we end up having to harbour him because otherwise he'd be extradited and subsequently executed.
You may be thinking to yourself that this is absurd, but the only unlikely aspect of this scenario is the escape, the rest is clearly true but also clearly ridiculous. This is the classic result of the thought experiment - reductio ad absurdum, the reduction of ones initial assumptions to an absurd conclusion.
Ordinarily this is used to prove that ones initial assumptions must be incorrect, and hopefully that the opposite assumption is correct. In physics or mathematics this technique is used to advance knowledge or dispense with theories that are wrong and we can move on, the better for things. Here we don't get to move on, instead we get to watch whilst the lawyers argue it out, the politicians who created the mess just watch and the rest of us stand with open mouths!